Two metal spheres of same mass are suspended from a common point by a light insulating string. The length of each string is same. The spheres are given electric charges $+q$ on one end and $+4q$ on the other. Which of the following diagrams best shows the resulting positions of spheres ?

The length of a metal wire is ${\ell }_1,$ when the tension in it is $T_1$ and is ${\ell }_2$ when the tension is $T_2.$ The natural length of the wire is:

Two blocks $A$ and $B$ are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on lower block $A$, so that $A$ and $B$ move without separation is $49 \mathrm{N}$. The coefficient of friction between $A$ and $B$ is

A particle moving with velocity $\overrightarrow{V}$ is acted by three forces shown by the vector triangle $PQR$. The velocity of the particle will

A maximum of $3 \mathrm{N}$ force can be applied on a block, down the incline, that would still not move the block which is placed on a rough inclined plane as shown in the figure. The maximum external force up the inclined plane that does not move the block is $12 \mathrm{N}$. The coefficient of static friction between the block and the plane is $\left[\mathrm{Take} g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

A rectangular frame of some mass has to be suspended symmetrically by two mass-less strings of equal length on two supports. It can be done in one of the three following ways as shown in below figures. The tension in the strings will be